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Permutations & Combinations

How many diff...

Question

How many different numbers of six digits can be formed with the number 3, 1, 7, 0, 9, 5 ?

A

500

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B

400

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C

300

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D

600

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Solution

The correct option is D 600
The number that can be formed, by taking digits together.
$=^{6} P_{6} = 6!$
But we have to neglect the number without with zero. Now the numbers in which zero with the $1^{s t}$ place = 5!
Hencw, the required number = 6!-5!
= 720 - 120 = 600.

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